Theoretical study of heterogeneous factors in epidemiological models

In epidemiology, or the study of public health in a population, theoretical approaches have been quite useful in the prevention or suppression of infectious diseases. Theoretical epidemiology consists of constructing mathematical and computational models, estimating parameters from statistical data, forecasting the spread of diseases, and examining the effectiveness of alternative policies. This gives estimates of key quantities such as basic reproductive number, final epidemic size and epidemic duration. Dynamics of susceptible, infected and recovered host, often called SIR model, and the diffusion process model describing the spread and the extinction of infectious diseases are the two classical models but still play important roles in theoretical epidemiology. Using the simplest SIR model, epidemic peak timing, prevalence at epidemic peak timing, final epidemic size and frequency of vaccinated host for prevention of outbreak can be solved analytically (Anderson and May 1991). However, this model is often difficult to apply directly to real epidemics, because of various factors causing heterogeneity. The basic SIR model includes many approximations and neglects heterogeneous factors. These simplifications sometimes are unrealistic when it is applied to real epidemics.I studied how different heterogeneous factors affect the dynamics and evolution of infectious diseases. I especially focus on the following three aspects: i) coevolution between host immunity and pathogen, ii) seasonality of epidemics, and iii) population dynamics of pathogen within hosts. 
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